How to change SQL instance name

All the doc's I've read shows to do the below, and restart SQL services, but I'm not able to login to the new SQL instance name--only the old one--and SQL config manager still shows the old instance name despite SELECT @@SERVERNAME returning the new instance name.

How do I get SQL server to recognize the new instance name when I run the below? This is a SQL 2012 instance.

sp_dropserver 'INSTANCE\OLD_NAME'  
go  
sp_addserver 'INSTANCE\NEW_NAME', 'local'  
go

Thanks